Zhihong Xia

Zhihong "Jeff" Xia (born September 20, 1962 in Dongtai , Jiangsu , People's Republic of China ) is a Sino-American mathematician . He is a professor at Northwestern University .

Life

Xia's construction in proving the Painlevé conjecture

Xia graduated from Nanjing University with a bachelor's degree in astronomy in 1982 and received a PhD in mathematics from Northwestern University in 1988 (The existence of non-collision singularities in Newtonian Systems). From 1988 to 1990 he was Assistant Professor at Harvard University , then until 1994 Associate Professor at the Georgia Institute of Technology (and Institute Fellow) and from 1994 Professor at Northwestern University. Since 2000 he has been Arthur & Gladys Pancoe Professor of Mathematics there.

He deals with celestial mechanics and dynamic systems. In his dissertation he solved an old problem of Paul Painlevé (Painlevé problem), the existence of singularities of non-collision character in the N-body problem in three-dimensional space, and he proved the existence for . To this end, he constructed an example of five masses, four of which orbit each other in two pairs in eccentric elliptical orbits around an axis of symmetry z and a fifth mass moves along the z-axis. For selected initial conditions, the fifth mass can escape into infinity in a finite time (without the bodies colliding with each other). The case N = 4 is open. For N = 3, however, Painlevé had proven that the singularities (points of the orbit where the forces diverge and which are reached in a finite time) must be of the collision type. However, his evidence could not be extended to the case . ${\ displaystyle N \ geq 5}$ ${\ displaystyle N> 3}$

In 1993 he was the first recipient of the American Mathematical Society's Blumenthal Award . From 1989 to 1991 he was a Sloan Research Fellow . From 1993 to 1998 he received the National Young Investigator Award from the National Science Foundation. In 1995 he received the Monroe Martin Award in Applied Mathematics from the University of Maryland.

Fonts

The Existence of Noncollision Singularities in Newtonian Systems, Annals of Mathematics, Series 2, Volume 135, 1992, pp. 411-468
with Donald G. Saari : Off to Infinity in Finite Time, Notices of the AMS, Volume 42, 1993, pp. 538-546, PDF (470 kB; English)

Web links

Homepage

Individual evidence

↑ The surprising fact that the existence of non-collision singularities in the N-body problem leads to two particles becoming infinitely far apart in a finite time, was proven in 1908 by Hugo von Zeipel
↑ Joseph L. Gerver gave arguments (a heuristic model) for the existence of non-collision singularities, a strict proof is missing. Gerver, Noncollision Singularities: Do Four Bodies Suffice ?, Exp. Math., Vol. 12, 2003, pp. 187-198, online

personal data
SURNAME	Xia, Zhihong
ALTERNATIVE NAMES	Xia, Jeff
BRIEF DESCRIPTION	Chinese-American mathematician
DATE OF BIRTH	20th September 1962
PLACE OF BIRTH	People's Republic of China

[1] The surprising fact that the existence of non-collision singularities in the N-body problem leads to two particles becoming infinitely far apart in a finite time, was proven in 1908 by Hugo von Zeipel

[2] Joseph L. Gerver gave arguments (a heuristic model) for the existence of non-collision singularities, a strict proof is missing. Gerver, Noncollision Singularities: Do Four Bodies Suffice ?, Exp. Math., Vol. 12, 2003, pp. 187-198, online